A diapycnal diffusivity model for stratified environmental flows

The vertical diffusivity of density, K-rho, regulates ocean circulation, climate and coastal water quality. K-rho is difficult to measure and model in these stratified turbulent flows, resulting in the need for the development of K-rho parameterizations from more readily measurable flow quantities. Typically, K-rho is parameterized from turbulent temperature fluctuations using the Osborn-Cox model or from the buoyancy frequency, N, kinematic viscosity, nu, and the rate of dissipation of turbulent kinetic energy, epsilon, using the Osborn model. More recently, Shih et al. (2005, J. Fluid Mech. 525: 193-214) proposed a laboratory scale parameterization for K-rho, at Prandtl number (ratio of the viscosity over the molecular diffusivity) Pr = 0.7, in terms of the turbulence intensity parameter, Re-b = epsilon/(nu N-2), which is the ratio between the destabilizing effect of turbulence to the stabilizing effects of stratification and viscosity. In the present study, we extend the SKIP parameterization, against extensive sets of published data, over 0.7 < Pr < 700 and validate it at field scale. Our results show that the SKIF model must be modified to include a new Buoyancy-controlled mixing regime, between the Molecular and Transitional regimes, where K-rho is captured using the molecular diffusivity and Osborn model, respectively. The Buoyancy-controlled regime occurs over 10(2/3)Pr(-1/2) < Re-b < (3 ln root Pr)(2), where K-rho = 0.1/Pr-1/4 nu Re-b(3/2) is Pr dependent. This range is shown to be characteristic to lakes and oceans and both the Osborn and Osborn-Cox models systematically underestimate K-rho in this regime. (C) 2013 Elsevier B.V. All rights reserved.